A Mathematical Introduction To Dirac S Formalism
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A Mathematical Introduction To Dirac S Formalism
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Author : S.J.L. van Eijndhoven
language : en
Publisher: Elsevier
Release Date : 1986-10-01
A Mathematical Introduction To Dirac S Formalism written by S.J.L. van Eijndhoven and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-10-01 with Mathematics categories.
This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part. The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.
Mathematical Introduction To Dirac S Formalism
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Author : S.J. Van Eijndhoven
language : it
Publisher:
Release Date :
Mathematical Introduction To Dirac S Formalism written by S.J. Van Eijndhoven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Many Faces Of Maxwell Dirac And Einstein Equations
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Author : Waldyr A. Rodrigues, Jr
language : en
Publisher: Springer
Release Date : 2016-04-26
The Many Faces Of Maxwell Dirac And Einstein Equations written by Waldyr A. Rodrigues, Jr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Science categories.
This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: “The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
From Spinors To Quantum Mechanics
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Author : Gerrit Coddens
language : en
Publisher: World Scientific
Release Date : 2015-06-29
From Spinors To Quantum Mechanics written by Gerrit Coddens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-29 with Science categories.
From Spinors to Quantum Mechanics discusses group theory and its use in quantum mechanics. Chapters 1 to 4 offer an introduction to group theory, and it provides the reader with an exact and clear intuition of what a spinor is, showing that spinors are just a mathematically complete notation for group elements. Chapter 5 contains the first rigorous derivation of the Dirac equation from a simple set of assumptions. The remaining chapters will interest the advanced reader who is interested in the meaning of quantum mechanics. They propose a novel approach to the foundations of quantum mechanics, based on the idea that the meaning of the formalism is already provided by the mathematics.In the traditional approach to quantum mechanics as initiated by Heisenberg, one has to start from a number of experimental results and then derive a set of rules and calculations that reproduce the observed experimental results. In such an inductive approach the underlying assumptions are not given at the outset. The reader has to figure them out, and this has proven to be difficult. The book shows that a different, bottom-up approach to quantum mechanics is possible, which merits further investigation as it demonstrates that with the methods used, the reader can obtain the correct results in a context where one would hitherto not expect this to be possible.
An Introduction To Dirac Operators On Manifolds
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Author : Jan Cnops
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Dirac Operators On Manifolds written by Jan Cnops and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhäuser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index
On Bras And Kets
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Author :
language : en
Publisher:
Release Date : 1969*
On Bras And Kets written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969* with categories.
The Many Faces Of Maxwell Dirac And Einstein Equations
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Author : Waldyr A. Rodrigues
language : en
Publisher: Springer
Release Date : 2010-11-25
The Many Faces Of Maxwell Dirac And Einstein Equations written by Waldyr A. Rodrigues and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Mathematics categories.
This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are solved in detail.
Trajectory Spaces Generalized Functions And Unbounded Operators
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Author : Stephanus van Eijndhoven
language : en
Publisher: Springer
Release Date : 2006-11-14
Trajectory Spaces Generalized Functions And Unbounded Operators written by Stephanus van Eijndhoven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Spinors In Four Dimensional Spaces
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Author : Gerardo F. Torres del Castillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-23
Spinors In Four Dimensional Spaces written by Gerardo F. Torres del Castillo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.
Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang–Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.
Quantum Theory
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Author : Peter Bongaarts
language : en
Publisher: Springer
Release Date : 2014-12-01
Quantum Theory written by Peter Bongaarts and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with Science categories.
This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.